U.S. crude prices jumped as much as 13 percent on Friday after a report once again suggested OPEC might finally agree to cut production to reduce the world glut, while a bounce in stock markets fed appetite for risk.

Despite the strong daily gain, oil prices were poised to end the week down with significant losses. But U.S. oil settled up more than 12 percent, for the best one-day gain since February 2009, when WTI gained 14.04 percent.

The about-turn came after one of the most volatile weeks for oil, with prices initially falling nearly 14 percent over a four-day stretch before springing back higher.

The United Arab Emirates' energy minister said the Organization of the Petroleum Exporting Countries was willing to cooperate on an output cut, the Wall Street Journal reported after Thursday's settlement in U.S. futures. He also said cheap oil was forcing supply reductions that would help rebalance the market.

The UAE's comments, coming after vain efforts earlier in the week by Venezuela and Russia to stir Saudi Arabia and other major producers into agreeing to output cuts, was initially greeted with skepticism by many traders.

But after a 75-percent price slump since mid-2014 that has taken crude prices to more than 12-year lows, many were also inclined to believe that a rebound was due sooner or later if production tightens or demand picks up.

"We expect declining U.S. oil production, in particular, to drive the oil price back up to $50 per barrel by the end of the year," Frankfurt-based Commerzbank said in a note.

U.S. benchmark West Texas Intermediate futures settled up $3.23, or 12.32 percent, at $29.44 a barrel, and was last trading up $2.83, or 10.76 percent, at $29.03 per barrel at at 3:29 p.m ET, off the day's high of $29.66. It hit a 12-year low of $26.05 in the previous session. For the week, it was on track for a 5.5 percent loss.

Brent was up $2.81, or 9.35 percent, at $32.89 per barrel. Weekly losses were pared to about 3.7 percent.

Crude prices extended gains after data showed an eighth straight weekly drop in the number of U.S. rigs drilling for oil. Oilfield services firm Baker Hughes reported its weekly rig count fell by 28 to a total of 439, compared with 1,056 rigs at this time last year.

Oil also got a boost from a rally in equity markets, with both U.S. and European shares rebounding from recent weakness.

Some cited Monday's Presidents Day's holiday in the United States, saying fewer players wanted to have a short position in oil ahead the longer weekend break for the New York crude market.

But others, like Tyche Capital Advisors' Tariq Zahir, were hoping to profit again from bearish bets once the rally peaks. "It gives me great opportunity to put out new shorts in crude spreads," he said.

Many expected wilder price swings in coming weeks.

"It's not a one-way price movement anymore," said ABN AMRO's senior energy economist Hans van Cleef. "We will see a period of high volatility".